Consider a system of two particles. Each particle can be in one of three possible microstates: one ground state (E = 0, call it "G") and two excited states (both with E = E, call them "A" and "B"). (a) List the possible states that this system can be in if both particles are bosons. (For example, "GG", "GA", and "AB" are three possibilities. Remember that AB and BA are the same state since these are indistinguishable particles.) Then write the partition function Z of this system as a function of β. (b) Now do the same thing if the particles are fermions.

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed